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PreprintarXiv licencearXiv

Pseudolocality of G2-Laplacian Flow

  • Weiyong He
  • Longhuan Yan
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Abstract

In this paper, we give a new proof of Perelman's pseudolocality theorem for Ricci flow, which does not rely on Perelman's Harnack-type inequality. The key step is an estimate relating initial local μ-entropy to pointed Nash entropy at later spacetime points. The argument also works for other reasonable geometric flows, like the G2-Laplacian flow, at a scale depending on its deviation from Ricci flow and its scalar curvature lower bound. As a consequence, we can also prove the quantitative rigidity results concerning pointed Nash entropy due to Hein-Naber and Bamler for such geometric flows. In the appendix, we also show that the other results in Bamler's work (arXiv:2008.07093), when suitably modified, remain valid for Laplacian flow with bounded torsion. These include log-Sobolev/Poincaré inequality for conjugate heat kernel measure, heat kernel estimates, and dependence of the pointed Nash entropy on its basepoint.

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Cite

BibTeXRIS
BibTeX
@misc{he2026pseudolocality,
  title = {{Pseudolocality of $G_2$-Laplacian Flow}},
  author = {Weiyong He and Longhuan Yan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38408},
  eprint = {2610.38408},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38408},
}
RIS
TY  - UNPB
TI  - Pseudolocality of G_2-Laplacian Flow
AU  - Weiyong He
AU  - Longhuan Yan
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38408
UR  - https://arxiv.org/abs/2610.38408
AB  - In this paper, we give a new proof of Perelman's pseudolocality theorem for Ricci flow, which does not rely on Perelman's Harnack-type inequality. The key step is an estimate relating initial local μ-entropy to pointed Nash entropy at later spacetime points. The argument also works for other reasonable geometric flows, like the G_2-Laplacian flow, at a scale depending on its deviation from Ricci flow and its scalar curvature lower bound. As a consequence, we can also prove the quantitative rigidity results concerning pointed Nash entropy due to Hein-Naber and Bamler for such geometric flows. In the appendix, we also show that the other results in Bamler's work (arXiv:2008.07093), when suitably modified, remain valid for Laplacian flow with bounded torsion. These include log-Sobolev/Poincaré inequality for conjugate heat kernel measure, heat kernel estimates, and dependence of the pointed Nash entropy on its basepoint.
ER  -